A DC-noise-free on-axis holographic display scheme using a phase-only spatial light modulator (SLM) is proposed. The origin of DC noise in the on-axis holographic display using a phase-only SLM is analyzed, and a DC noise rejection filter is optimized for a phase-only SLM is designed. A novel two-step iterative Fourier transform algorithm for the optimal synthesis of a phase-only computer-generated hologram using the proposed scheme is devised. The proposed scheme and algorithm are validated with numerical simulations and experiments.